PP-wave Black holes and The Matrix Model

We discuss the sizes of a black hole in the M theory pp-wave background, and how the transverse size can be reproduced in the matrix model. Dec. 2002 PP-wave backgrounds, as a limit of AdS and some inner spheres, have proven an interesting place to test ideas of holography and the correspondence between string/M theory in such a background and some supersymmetric gauge theory [1]. In a previous paper [2], we discussed possible correspondence between string states and black hole states in such a background, when the string coupling is fined tuned for a given total oscillation number of the strings. As we shall see, the estimate of the transverse gravitational size of a black hole in that paper is correct, but the longitudinal size given there is incorrect. In the original paper, the first paper in [1], a matrix model is given for the PP-wave background obtained from the M theory AdS backgrounds. This matrix model was further